Commit 121fe5fc authored by Daniel Brown's avatar Daniel Brown
Browse files

Merge branch 'master' of gitmaster.atlas.aei.uni-hannover.de:pykat/pykat

parents 9212e608 06194b20
import numpy as np
from scipy.misc import factorial as fac
import math
def zernike_R(m, n, rho):
......@@ -36,3 +37,75 @@ def zernike(m, n, rho, phi):
else:
return zernike_R(0, n, rho)
def znm2Rc(A,R):
'''
Convertes amplitudes of Zernike polynomials of order n=2 into
spherical radius of curvature. In case the astigmatic modes
(m=-1,m=2) are included, the functon returns the maximum and
minimum curvature.
Inputs: A, R
A - List of amplitudes of order 2 Zernike polynomials, ordered so that m
increases with list index. 1 <= len(A) <= 3. [m]
R - Radius of the mirror surface in the xy-plane. [m]
Returns: Rc
Rc - If astigmatic modes are used (len(A) == 2 or 3) a numpy.array of length
2 containing max and min curvatures is returned. If only the 'defocus'
mode is used Rc is a float number. [m]
Based on the Simtools function 'FT_Znm_to_Rc.m' by Charlotte Bond.
'''
if isinstance(A,list):
if len(A)==3:
a20 = A[1]
a22 = math.sqrt(A[0]**2 + A[2]**2)
s = np.array([1.0, -1.0])
elif len(A)==2:
a20 = 0
a22 = math.sqrt(A[0]**2 + A[1]**2)
s = np.array([1.0, -1.0])
elif len(A)==1:
a20 = A[0]
a22 = 0
s = 0
elif isinstance(A,float) or isinstance(A,int):
a20 = A
a22 = 0
s = 0
Rc = ((2*a20 + s*a22)**2 + R**2)/(2*(2*a20+s*a22))
return Rc
def Rc2znm(Rc,R):
'''
Converts Radius of curvatue to amplitudes of the second order Zernike
polynomials.
Iputs: Rc, R
Rc - Radius of curvature. Either a number or a numpy.ndarray with
minimum and maximum curvature.
R - Radius of mirror in xy-plane.
Returns: A
A - Ampltude(s) of the second order Zernike polynomials needed. Is
a number if Rc is a number, and if R is a numpy.ndarray so is A.
Based on Simtools function 'FT_Rc_to_Znm.m' by Charlotte Bond.
'''
# Amplitude in x and y directions
c = ( Rc - np.sign(Rc)*np.sqrt(Rc**2 - R**2) )/2
if isinstance(Rc, np.ndarray):
A = np.array([])
# Adding Z(2,0) amplitude
A = np.append(A,c.mean())
# Adding Z(2,2) amplitude
A = np.append(A,2*(c[0]-A[0]))
elif isinstance(Rc, float) or isinstance(Rc, int):
A = c
return A
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